I have had this problem before (in fact, upon joining the org it was the first question I asked). What has happened is that the game file has become corrupted. Your kings influence (and any subsequent kings) will jump all over the place for ever. Nothing you can do to salvage that game. This was a very major problem for me, but there are several ways to reduce it. It is linked to the quicksave file, basically the more you go on in time and the more the quicksave file has been overwritten the more chance it has of becoming corrupted. To prevent it;
1. TURN AUTOSAVE OFF. This also overwrites saves files, and so can cause the game file to become corrupted.
2. ONLY QUICKSAVE AT THE START OF THE TURN. Annoying, yes, I want to quicksave once all my moves are done but if you do that then there is additional data being saved that may cause it to go buggy (late in the game). Quicksaving at the start of every turn will not cause the file to go buggy.

Ever since I have done this I have never experienced jumping influence. Do these and you too can enjoy a steady Kings influence